Crystallization means you allow the liquid to cool at a rate slow enough to form crystals (ie, produce stable, long range order of atoms/molecules). Solidification can produce a crystal or not. For example, when you make a thermal quenching of a fused silica mixture, you get a glass, when you allow to slowly cool the same mixture, you could get quartz-like crystals. When you cool a liquid metal you obtain a solid that usually is crystalline. When you cool liquid asphalt, you get solid asphalt that usually is amorphous. Hope it is useful.

Crystakllization is a method of purification of a substance bu solidificsation is a method of seperation from other materials resulting inpreparation of a compound.

Crystallization means you allow the liquid to cool at a rate slow enough to form crystals (ie, produce stable, long range order of atoms/molecules). Solidification can produce a crystal or not. For example, when you make a thermal quenching of a fused silica mixture, you get a glass, when you allow to slowly cool the same mixture, you could get quartz-like crystals. When you cool a liquid metal you obtain a solid that usually is crystalline. When you cool liquid asphalt, you get solid asphalt that usually is amorphous. Hope it is useful.

Solidification usually aplly to a melt of a substance: when you have a nearly pure substance in a melt state it will solidy when you cool the system. This is also known as melt crystallization.

Crystallization is usually used to refer a generation of a solid from a solution: when you have a substance dissolved in a solvent you can recover it by forming a two phase system by elevation of the concentration of dissolved solid above the solution saturation ( by evaporation, cooling, addition of a non solvent, etc.)

“Solidification or crystallization occurs when atoms are transformed from the disordered liquid state to the more ordered solid state, and is fundamental to metals processing.”

See: “Solidification and Crystallization Processing in Metals and Alloys” by Hasse Fredriksson, Ulla Akerlind, ISBN: 978-1-119-99305-6, 826 pages, August 2012

may I add another coment on your question:

When you solidify or even crystallize a substance you not necessarilly will take a solid phase crystalline. If a solid phase is too fast formed, you can have an amorphous material in same cases.

See:

Figure 4.1 Solidification versus crystallization (after Zallen 1983).

in:

“Lanthanide trifluoride thin films: Structure, composition, and optical properties” by

Lingg, Linda Jeanne

http://arizona.openrepository.com/arizona/bitstream/10150/185031/1/azu_td_9024650_sip1_m.pdf

Thanks a lot for all of your valuable time. I have understood the difference between the both.

i exactly agree with mr F. Caballero-Briones

The term solidification represents the transition between a liquid phase (without peculiar shape) to a solid one (with its own peculiar shape); in a liquid atoms or molecules have three degrees of freedom (translational, rotational and vibrational), while in a solid the translation are practically  zero. A solid, in turn, can be amorphous or crystallized, according to the presence of lattice properties (crystal) such as the periodicity and the finite number of symmetry elements.